subroutine figi2(nm,n,t,d,e,z,ierr)
c
integer i,j,n,nm,ierr
real t(nm,3),d(n),e(n),z(nm,n)
real h
c
c given a nonsymmetric tridiagonal matrix such that the products
c of corresponding pairs of off-diagonal elements are all
c non-negative, and zero only when both factors are zero, this
c subroutine reduces it to a symmetric tridiagonal matrix
c using and accumulating diagonal similarity transformations.
c
c on input
c
c nm must be set to the row dimension of two-dimensional
c array parameters as declared in the calling program
c dimension statement.
c
c n is the order of the matrix.
c
c t contains the input matrix. its subdiagonal is
c stored in the last n-1 positions of the first column,
c its diagonal in the n positions of the second column,
c and its superdiagonal in the first n-1 positions of
c the third column. t(1,1) and t(n,3) are arbitrary.
c
c on output
c
c t is unaltered.
c
c d contains the diagonal elements of the symmetric matrix.
c
c e contains the subdiagonal elements of the symmetric
c matrix in its last n-1 positions. e(1) is not set.
c
c z contains the transformation matrix produced in
c the reduction.
c
c ierr is set to
c zero for normal return,
c n+i if t(i,1)*t(i-1,3) is negative,
c 2*n+i if t(i,1)*t(i-1,3) is zero with
c one factor non-zero.
c
c questions and comments should be directed to burton s. garbow,
c mathematics and computer science div, argonne national laboratory
c
c this version dated august 1983.
c
c ------------------------------------------------------------------
c
ierr = 0
c
do 100 i = 1, n
c
do 50 j = 1, n
50 z(i,j) = 0.0e0
c
if (i .eq. 1) go to 70
h = t(i,1) * t(i-1,3)
if (h) 900, 60, 80
60 if (t(i,1) .ne. 0.0e0 .or. t(i-1,3) .ne. 0.0e0) go to 1000
e(i) = 0.0e0
70 z(i,i) = 1.0e0
go to 90
80 e(i) = sqrt(h)
z(i,i) = z(i-1,i-1) * e(i) / t(i-1,3)
90 d(i) = t(i,2)
100 continue
c
go to 1001
c .......... set error -- product of some pair of off-diagonal
c elements is negative ..........
900 ierr = n + i
go to 1001
c .......... set error -- product of some pair of off-diagonal
c elements is zero with one member non-zero ..........
1000 ierr = 2 * n + i
1001 return
end